Question

This is a check of whether I did everything right rather than a direct question: (below, one minute.)

Answer 1

\[f(x) = \ln(x-1), [2,4].\](Application of the Mean Value Theorem), find the value of c that satisfies it.)\[f'(x) = \frac{ 1 }{ x-1 }\]\[f(b)=\ln(4-1) = \ln(3)\]\[f(a)=\ln(2-1)=\ln(1)=0\]
\[f'(x) = \frac{ f(b) - f(a) }{ b-a }\]\[\frac{ 1 }{ x-1 }=\frac{ \ln(3)-(0) }{ 4-2 }=\frac{ \ln(3) }{ 2 }\]\[\frac{ 2 }{ x-1 }=\ln(3)\]\[x-1 = \frac{ 2 }{ \ln(3) }\]\[x = \frac{ 2 }{ \ln(3) }+1\]Does this look right to everyone?

Answer 2

looks good.

Answer 3

Kay, thanks.